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math.DG2023
Universal Liouville action as a renormalized volume and its gradient flow
Martin Bridgeman, Kenneth Bromberg, Franco Vargas Pallete +1
The universal Liouville action (also known as the Loewner energy for Jordan curves) is a Kähler potential on the Weil-Petersson universal Teichmüller space, which is identified wit…
math.DG2017★ 14 cited
Schwarzian derivatives, projective structures, and the Weil-Petersson gradient flow for renormalized volume
Martin Bridgeman, Jeffrey Brock, Kenneth Bromberg
To a complex projective structure on a surface, Thurston associates a locally convex pleated surface. We derive bounds on the geometry of both in terms of the norms $\|ϕ_Σ\|_\i…